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Chapter 36, Problem 10P

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Which of the following sets of quantum numbers can be used to describe the 2 electrons in the He atom? For the possible sets, write the electron configuration and identify if it is a ground state or excited state configuration. i) n = 2,1 = 0, mį = 0, mş = 1/2 and n = 1, 1 = 0, m = 0, mş = 1/2 ii) n = 2,1= 0, mi = 0, ms = 1/2 and n = 2,1= 0, mi = 0, ms = 1/2 iii) n = 2,1= 1, mị = 0, mş = 1/2 and n = 2,1= 0, mį = 0, ms = 1/2 iv) n = 2,1= 0, mį = 0, ms =- 1/2 and n = 2,1= 0, m¡ = 0, ms = 1/2 v) n = 1,1= 0, mį = 0, mş = 2 and n = 1,1 = 0, mį = 0, mş = -2 %3D %3D %3D %3D

Angular momentum and Spin. An electron in an H-atom has orbital angular momentum magnitude and z-component given by L² = 1(1+1)ħ², Lz = m₁h, 1 = 0,1,2,..., n 1 - m₁ = 0, ±1, ±2, ..., ±l 3 S² = s(s+1) h² = =h²₁ 4 Consider an excited electron (n > 1) on an H-atom. The total angular momentum ] = L + Š, whose magnitude and z-component follow a similar dependence to some quantum numbers j and m; as J² = j(j + 1)ħ², Jz = mjħ 1 S₂ = m₂h = ± = h Where j and m; are quantum numbers which assume values that jumps in steps of one such that j is non-negative and −j ≤ m¡ ≤ j. For a given quantum number 1, what are the (two) possible values for j? Clue: we can use the vector sum relation of angular momenta, then consider the z-component only.

Consider the atom having the electron configuration 1s2 2s2 2p6 3s2. Assume that the z components of both the orbital abd spin angular momenta of the electron in the 3p subshell are positive. What are the quantum numbers that describe the state of this electron. n=3 l=1 m=-1 s=1/2n=3 l=1 m=2 s=1/2n=3 l=2 m=1 s=1/2n=3 l=1 m=1 s=1/2n=3 l=2 m=2 s=-1/2 Can we say which one is correct?